I did not follow a rigorous routine when it came to routing the underside of the keys to tune them.  However, by trial and error I did discover a few important principles that I feel I ought to pass on.

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1. Don't cut too wide

 

The first is that you should try not to route away material from too close to the drilled holes that correspond with the nodes. This is mostly aesthetic but it does help to support the keys depending on the design of your instrument.  I used a rule of thumb of not encroaching over a line drawn at 25% from the ends of the key.

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2. Don't cut too thin

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The second point is that you should try not to cut the keys too thin.  As a rule of thumb the main cut (which extends between the two 25% lines) did not go deeper than 6mm.  The second cut, more or less between the 40% lines, was set at about 12mm.  As the keys were made of wood that was 22 to 23mm thick, this means that I tried to leave at least 1cm of wood across the middle of the bar.  This rule held true for a majority of the notes, although for the three lowest notes - G2, A2 and B2 - I was not able to keep to these guidelines, which accounts for why these notes are a little ropey compared to the others I produced.

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In fact I experimented with a number of different cuts, sometimes performing four different cuts between the 25% lines, the 30% lines, the 35% lines and the 40% lines....but I tried never to leave less than a centimetre of wood at the thinnest point, except when fine tuning using a file and sandpaper.  

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3. The closer you are to the middle, the less material you need to remove to make a significant change to the frequency

 

Basically, removing material from the underside weakens the torsional strength of the wood so that the bar becomes more elastic and flexible.  As a result it vibrates less frequently, lowering the pitch of the note it produces when struck.  However, removing material also reduces the mass of the bar which conversely causes a slight increase in the vibration rate.  This means that removing material will both lower the pitch and slightly raise the pitch at the same time.  The lowering effect is larger, but it does mean that it can be frustrating trying to get a marimba key in tune.

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4.  Fine tune the key by filing away a thin channel from the middle of the bar

 

The router can only tune to within tens of Hertz.  The last few Hertz need to be fine tuned by filing away a channel from the very centre of the arch.   Be very careful when doing this as it is easy to make the note too flat.

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5.  Take from the ends if the note goes flat

 

You can remove material from the ends of the bar to raise the pitch slightly.  However, the effect of this is very small compared to the material you remove.  Don't count on this technique to salvage bars you have caused to go flat!  Removing material lowers the mass, but this changes the behaviour of the bar and it never sounds quite as good as it did before you took too much material away....and now that it is flat and cannot be brought back to pitch, you cannot use it to make a lower note because it is the wrong length and has already got holes in it at its nodes that will not correspond to the require intervals to sit on the rails in a different position....so the bar is destined for the bone yard....

 

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6.  Don't get hung up on the harmonics

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A flat bar with no arch will not generate any harmonics because it is limited in the way it flexes.  However, trying to tune the harmonics of a marimba key is a process that takes lots and lots of practice.  Of all the 27 notes I produced, about 7 or 8 have the first harmonic tuned and only one or two have the second harmonic tuned as well.  However, the marimbasI have made are perfectly suitable fore my students to play in school.  In the meantime I can continue producing new keys, replace them if and when they are an improvement on the original.

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